Number & Operations (N)

A2.N.1 Extend the understanding of number and operations to include complex numbers, matrices, radical expressions, and expressions written with rational exponents

A2.N.1.1 Find the value of i^{n} for any whole number n.

A2.N.1.2 Simplify, add, subtract, multiply, and divide complex numbers.

A2.N.1.3 Use matrices to organize and represent data. Identify the order (dimension) of a matrix, add and subtract matrices of appropriate dimensions, and multiply a matrix by a scalar to create a new matrix to solve problems. 
A2.N.1.4 Understand and apply the relationship of rational exponents to integer exponents and radicals to solve problems.

Algebraic Reasoning & Algebra (A)

A2.A.1 Represent and solve mathematical and realworld problems using nonlinear equations and systems of linear equations; interpret the solutions in the original context.

A2.A.1.1 Represent realworld or mathematical problems using quadratic equations and solve using various methods (including graphing calculator or other appropriate technology), factoring, completing the square, and the quadratic formula. Find nonreal roots when they exist.

A2.A.1.2 Represent realworld or mathematical problems using exponential equations, such as compound interest, depreciation, and population growth, and solve these equations graphically (including graphing calculator or other appropriate technology) or algebraically

A2.A.1.3 Solve onevariable rational equations and check for extraneous solutions. 
A2.A.1.4 Solve polynomial equations with real roots using various methods and tools that may include factoring, polynomial division, synthetic division, graphing calculators or other appropriate technology 
A2.A.1.5 Solve square root equations with one variable and check for extraneous solutions. 
A2.A.1.6 Solve common and natural logarithmic equations using the properties of logarithms.

A2.A.1.7 Solve realworld and mathematical problems that can be modeled using arithmetic or finite geometric sequences or series given the n^{th} terms and sum formulas. Graphing calculators or other appropriate technology may be used. 
A2.A.1.8 Represent realworld or mathematical problems using systems of linear equations with a maximum of three variables and solve using various methods that may include substitution, elimination, and graphing (may include graphing calculators or other appropriate technology). 
A2.A.1.9 Solve systems of equations containing one linear equation and one quadratic equation using tools that may include graphing calculators or other appropriate technology. 
A2.A.2 Represent and analyze mathematical situations and structures using algebraic symbols using various strategies to write equivalent forms of expressions.

A2.A.2.1 Factor polynomial expressions including but not limited to trinomials, differences of squares, sum and difference of cubes, and factoring by grouping using a variety of tools and strategies.

A2.A.2.2 Add, subtract, multiply, divide, and simplify polynomial and rational expressions 
A2.A.2.3 Recognize that a quadratic function has different equivalent representations [f(x) = ax^{2 }+ bx + c, f(x) = a(x − ℎ)^{2} + k, and f(x) = (x − ℎ)(x − k)]. Identify and use the representation that is most appropriate to solve realworld and mathematical problems.

A2.A.2.4 Rewrite expressions involving radicals and rational exponents using the properties of exponents.

Functions (F)

A2.F.1 Understand functions as descriptions of covariation (how related quantities vary together).

A2.F.1.1 Use algebraic, interval, and set notations to specify the domain and range of functions of various types and evaluate a function at a given point in its domain.

A2.F.1.2 Recognize the graphs of exponential, radical (square root and cube root only), quadratic, and logarithmic functions. Predict the effects of transformations [f(x + c), f(cx) + c, f(cx), and cf(x), where ! is a positive or negative realvalued constant] algebraically and graphically, using various methods and tools that may include graphing calculators or other appropriate technology.

A2.F.1.3 Graph a quadratic function. Identify the x and yintercepts, maximum or minimum value, axis of symmetry, and vertex using various methods and tools that may include a graphing calculator or appropriate technology

A2.F.1.4 Graph exponential and logarithmic functions. Identify asymptotes and x and yintercepts using various methods and tools that may include graphing calculators or other appropriate technology. Recognize exponential decay and growth graphically and algebraically. 
A2.F.1.5 Analyze the graph of a polynomial function by identifying the domain, range, intercepts, zeros, relative maxima, relative minima, and intervals of increase and decrease. 
A2.F.1.6 Graph a rational function and identify the x and yintercepts, vertical and horizontal asymptotes, using various methods and tools that may include a graphing calculator or other appropriate technology. (Excluding slant or oblique asymptotes and holes.) 
A2.F.1.7 Graph a radical function (square root and cube root only) and identify the x and yintercepts using various methods and tools that may include a graphing calculator or other appropriate technology. 
A2.F.1.8 Graph piecewise functions with no more than three branches (including linear, quadratic, or exponential branches) and analyze the function by identifying the domain, range, intercepts, and intervals for which it is increasing, decreasing, and constant 
A2.F.2 Analyze functions through algebraic combinations, compositions, and inverses, if they exist.

A2.F.2.1 Add, subtract, multiply, and divide functions using function notation and recognize domain restrictions.

A2.F.2.2 Combine functions by composition and recognize that g(x) = f^{1}(x), the inverse function of fx), if and only if g(f(x)) = x. 
A2.F.2.3 Find and graph the inverse of a function, if it exists, in realworld and mathematical situations. Know that the domain of a function f is the range of the inverse function f^{1}, and the range of the function is the domain of the inverse function f^{1}. 
A2.F.2.4 Apply the inverse relationship between exponential and logarithmic functions to convert from one form to another.

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